A non-lauric, non-trans, non-temper (Non-LTT) fat composition comprising a fraction obtained from a randomised triglyceride mixture in which min. 90% by weight of the constituent fatty acids are: palmitic (C16:0), stearic (C18:0), arachidic (C20:0) behenic (C22:0), oleic (C18:1) and linoleic (C18:2) acid and the total content of arachidic and behenic acid is 3-40% by weight and the total content of palmitic and stearic acids is 25-60% by weight, said fraction having the following physical and chemical properties: (1) slip melting point measured according to AOCS Cc 3-25: below 36.degree. C. and solid fat content (SFC) measured according to IUPAC 2.150 mod. (stabilised at 20.degree. C. for 24 h): above 25% by weight at 20.degree. C.; (2) total content of saturated fatty acids measured according to IUPAC 2.301 and 2.304: 40-75% by weight, preferably 45-70% by weight; (3) total content of arachidic and behenic acids: 3-40% by weight, preferably 5-35% by weight, and total content of palmitic and stearic acids: 25-60% by weight, preferably 25-50% by weight, both measured according to IUPAC 2.301 and 2.304; (4) total content of triglycerides having triglyceride composition (TGC) of C56-C60 measured by number of total carbon atoms of constituent fatty acids according to IUPAC 2.323: min. 9% by weight, preferably min. 15% by weight; (5) total content of S.sub.2U-type triglycerides: min. 25% by weight, preferably min. 35% by weight, where S=saturated fatty acids and U=unsaturated fatty acids.